Related papers: Variance Control in Weak Value Measurement Pointer…

One of the most intriguing aspects of Quantum Mechanics is the impossibility of measuring at the same time observables corresponding to non-commuting operators. This impossibility can be partially relaxed when considering joint or…

In contrast to that a weak value of an observable is usually divided into real and imaginary parts, here we show that separation into modulus and argument is important for modular values. We first show that modular values are expressed by…

We introduce contextual values as a generalization of the eigenvalues of an observable that takes into account both the system observable and a general measurement procedure. This technique leads to a natural definition of a general…

It is demonstrated that a weak measurement of the squared quadrature observable may yield negative values for coherent states. This result cannot be reproduced by a classical theory where quadratures are stochastic $c$-numbers. The real…

We re-examine the status of the weak value of a quantum mechanical observable as an objective physical concept, addressing its physical interpretation and general domain of applicability. We show that the weak value can be regarded as a…

Weak convergence of probability measures is one of the most important topics in the field probability and statistics. In this survey paper, we look at weak convergence of probability measures from the topological vector space point of view.…

In this paper we propose a setup for the weak measurement of photon arrival time. It is found that the weak values of this arrival time can lie far away from the expectation value, and in principle also in regions forbidden by special…

When the weak value of a projector is 1, a quantum system behaves as in that eigenstate with probability 1. By definition, however, the weak value may take an anomalous value lying outside the range of probability like -1. From the…

In the late 80s, a curious effect suggested by Aharanov, Albert and Vaidman opened up new vistas regarding quantum measurements on weakly coupled systems. There, a combination of a "weak" finite interaction together with a "strong"…

This paper starts with a brief review of the topic of strong and weak pre- and post-selected (PPS) quantum measurements, as well as weak values, and afterwards presents original work. In particular, we develop a nonperturbative theory of…

A joint characterisation of the controllability and observability of a particular kind of discrete system has been developed. The key idea of the procedure can be reduced to a correct choice of the sampling sequence. This freedom, owing to…

When you measure an observable, A, in Quantum Mechanics, the state of the system changes. This, in turn, affects the quantum-mechanical uncertainty in some non-commuting observable, B. The standard Uncertainty Relation puts a lower bound on…

We review the definition and the concepts of the weak values and some measurement model to extract the weak value. This material is based on the author Ph.D. thesis "Time in Weak Values and Discrete Time Quantum Walk" at Tokyo Institute of…

A general formalism for joint weak measurements of a pair of complementary observables is given. The standard process of optical three-wave mixing in a nonlinear crystal (such as in parametric down-conversion) is suitable for such tasks. To…

In a weak measurement with post-selection, a measurement value, called the weak value, can be amplified beyond the eigenvalues of the observable. However, there are some controversies whether the weak value amplification is practically…

The transition from von Neumann's projective strong measurement to Aharonov's weak measurement has recently received large attention, theoretical and experimental. In this work, we present a general approach to describe the weak-to-strong…

Time averaging of weak values using the quantum transition path time probability distribution enables us to establish a general uncertainty principle for the weak values of two not necessarily Hermitian operators. This new principle is a…

When a well-localized photon is incident on a spatially superposed absorber but is not absorbed, the photon can still deliver energy to the absorber. It is shown that when the transferred energy is small relative to the energy uncertainty…

Post-selected weak measurement has been widely used in experiments to observe weak effects in various physical systems. However, it is still unclear how large the amplification ability of a weak measurement can be and what determines the…

Quantum measurement remains a puzzle through its stormy history from the birth of quantum mechanics to state-of-the-art quantum technologies. Two complementary measurement schemes have been widely investigated in a variety of quantum…